Free Printable Circle

1.

Equation of circle with center at origin with radius 'a'

a)

$x^2+y^2=a^2$

b)

$x^2+y^2=r^2$

c)

$x^2-y^2=a^2$

d)

$y^2-x^2=a^2$

2.

Equation of a circle with centre (h,K) and radius 'r'

a)

$\left(x-h\right)^2+\left(y-k\right)^2=a^2$

b)

$\left(x-k\right)^2+\left(y-h\right)^2=r^2$

c)

$\left(x-h\right)^2+\left(y-k\right)^2=r^2$

d)

$\left(x+h\right)^2+\left(y-k\right)^2=a^2$

3.

General equation of circle

a)

$x^2+y^2=a^2$

b)

$\left(x-h\right)^2+\left(y-k\right)^2=r^2$

c)

$x^2+y^2+2gx+2fy+c=0$

d)

$x^2-y^2+2gx-2fy-c=0$

4.

Equation of circle in diameter form

a)

$\left(x-x_1\right)\left(x-x_2\right)+\left(y-y_1\right)\left(y-y_2\right)=0$

b)

$x^2+y^2=a^2$

c)

$\left(x-h\right)^2+\left(y-k\right)^2=a^2$

d)

$\left(x-x_1\right)\left(x-x_2\right)-\left(y-y_1\right)\left(y-y_2\right)=0$

5.

Determine the equation of the circle if the ends of a diameter be at $\left(1,2\right)$ and $\left(3,5\right).$

a)

$x^2+y^2-4y-6x-12=0$

b)

$y^2-x^2=2y$

c)

$x^2-y^2+3y=0$

d)

$x^2+y^2-4x-6y+13=0$

6.

$2x^2+2y^2-12x+4y=1$ Find the centre and the radius of the circle

a)

$C=\left(3,-1\right),\ r=\frac{\sqrt{41}}{2}$

b)

$C=\left(2,4\right),\ r=4$

c)

$C=\left(3,2\right),\ r=2$

d)

$C=\left(2,-1\right),\ r=\frac{5}{3}$

7.

Find the equation of the circle which has centre at (a,b) and touches y-axis.

a)

$x^2+y^2-2ay=0$

b)

$x^2+y^2-2ax-2by+b^2=0$

c)

$x^2-y^2-2by=0$

d)

$x^2+y^2-3ax-4by=0$

8.

Find the equation of a circle whose two of the diameters are $x+y=6$ and $x+2y=4$ and radius 10.

a)

$x^2+y^2-3x+2y=0$

b)

$x^2+y^2-14x+3y=32$

c)

$x^2+y^2-16x+4y-32=0$

d)

$x^2-y^2-2x+4y-22=0$

9.

Find the equation of the circle which touches the coordinate axes at (a,0) and (0,a).

a)

$x^2+y^2-2ax-2ay+a^2=0$

b)

$x^2-2xy+y^2=0$

c)

$x^2+y^2=4xy$

d)

$x^2+y^2-4xy+3x-4y=0$

10.

Find the equation of a the circle which is concentric to the circle $x^2+y^2-8x+12y+15=0$ and passes through (5,4).

a)

$x^2+y^2-8x+12y-49=0$

b)

$x^2-y^2+3x+4y-5=0$

c)

$x^2-y^2+5x-5y=0$

d)

$x^2-y^2+5x-10y=0$

11.

Find the equation of the circle which touches both axes and has its centre on the line $x-2y=3.$

a)

$x^2+y^2+6x+6y+9=0$

b)

$x^2-y^2+3x-4y=0$

c)

$x^2-y^2+5x-5y-7=0$

d)

$x^2-2xy-4y^2-7x=0$

12.

Find the equation of the circle which touches the x-axis at (4,0) and passes through the point (1,1)

a)

$x^2-y^2+2xy-3x=5$

b)

$x^2-y^2+x-5y=9$

c)

$x^2-y^2-4x+3y-5=0$

d)

$x^2+y^2-8x-10y+16=0$

13.

Find the equation of the circle which has its centre on the line y=2 and passes through the points (2,0), (4,0).

a)

$x^2+y^2-2x=5$

b)

$x^2+y^2-16x+4y-32=0$

c)

$x^2+y^2-6x-4y+8=0$

d)

$x^2+y^2-5x+2y-9=0$

14.

This is a picture of ___________.

a)

Chord

b)

Diameter

c)

Radius

d)

Inscribed Angle

15.

The distance from the center of a circle to the boundary of a circle (half of the diameter).

a)

Chord

b)

Diameter

c)

Radius

d)

Inscribed Angle

16.

A segment with 2 endpoints on the circle.

a)

Chord

b)

Diameter

c)

Radius

d)

Inscribed Angle

17.

This is a picture of ___________.

a)

Chord

b)

Diameter

c)

Radius

d)

Inscribed Angle

18.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

19.

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

a)

Center (4,3)
Radius = 5 units

b)

Center (4,3)
Radius = 25 units

c)

Center (-4,-3)
Radius = 25 units

d)

Center (-4,-3)
Radius = 5 units

20.

Write the standard equation of the circle with the given center and radius; center (0,0) and radius: 3

a)

x²+y²=4

b)

x²+y²=81

c)

x²+y²=9

21.

What is the radius of the circle with this equation x² + y² - 10x + 8y - 23 = 0?

a)

4

b)

2

c)

8

d)

23

22.

What is the center for the circle with this equation x² + y² + 4x + 6y - 36 = 0?

a)

(-2, 5)

b)

(2, 7)

c)

(-2, -7)

d)

(-2, -3)

23.

A tangent is a line that _______.

a)

passes through the center of the circle

b)

intersects the circle at two points

c)

intersects the circle at one point

d)

follows the circumference of a circle

24.

The definition of a circle is

a)

set of all points in a plain that are the same distance from a point called the center

b)

the distance around a share

c)

a large figure

d)

a pizza, orange, plum, or watermelon

25.

What is the center of the circle with equation x² + y² = 1?

a)

(1, 1)

b)

(0, 0)

c)

not enough information

26.

What is the center of a circle with equation (x-4)² + y² = 5?

a)

(-4, 0)

b)

(4, 0)

c)

(4, 1)

d)

(-4, 1)

27.

A tangent to a circle is ________________________ to the radius drawn to the point of tangency.

a)

congruent

b)

perpendicular

c)

complimentary

d)

supplementary

Circle

Total questions: 27

Worksheet time: 49mins

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